Answer
$sin\beta=-\frac{1}{\sqrt 10}=-\frac{\sqrt 10}{10}$
$cos\beta=-\frac{3}{\sqrt 10}=-\frac{3\sqrt 10}{10}$
$tan\beta=\frac{1}{ 3}$
$csc\beta=-\sqrt 10$
$sec \beta=-\frac{\sqrt 10}{3}$
Work Step by Step
Since $cot\beta=3$, we can label the adjacent side as having length 3 and the opposite side as having length 1.
The Pythagorean Theorem gives
hypotenuse side$=\sqrt {3^{2}+1^{2}}=\sqrt 10$
The other five trigonometric functions are given as follows:
$sin\beta=-\frac{1}{\sqrt 10}=-\frac{\sqrt 10}{10}$
$cos\beta=-\frac{3}{\sqrt 10}=-\frac{3\sqrt 10}{10}$
$tan\beta=\frac{1}{ 3}$
$csc\beta=-\sqrt 10$
$sec \beta=-\frac{\sqrt 10}{3}$
